I Vibed a Proof of Conway's Conjecture
3 hours ago
- The author spent a month using AI models (Claude, ChatGPT, Codex) to solve Conway's refinement conjecture about omnific integers, a problem posed by John Conway 50 years ago.
- The proof was formalized in Lean and passed mechanical checks, though it has not yet been independently verified by mathematicians.
- The initial attempts involved instructing AI agents to solve the problem directly, but these often produced hallucinated or flawed results, leading to a restart.
- The project required setting up multi-agent systems for division of labor, including Lean verification, mathematical reasoning, and auditing roles.
- Key insights came from having AI agents critique and correct each other's work, though many ideas needed to be rediscovered multiple times due to being lost or rejected.
- The author learned that AI can be effective for proof formalization but struggles with mathematical creativity and self-evaluation, making human oversight crucial.
- The process cost an estimated $40,000 in API tokens (around 40 billion total) and highlighted challenges in distinguishing genuine progress from AI-generated 'bullshit'.
- The proof remains complex and difficult to simplify, but the author hopes to make it more accessible to mathematicians and Lean users in the future.
- The author concludes that while the experiment shows potential for 'vibecoding' math with AI, it requires significant time, token investment, and careful project management.